I already know the lowest one. (Phione with the same stats as Glalie) But which one has the highest? Remember that Other Forms count.
Mega Mewtwo X&Y and Mega Rayquaza tie in 1st with a whopping 780 base stat.
Source: CLICK ME
As of Generation 8, Eternamax Eternatus is now the legendary with the highest BST, at 1125. This form is unusable, however. The previous answer is still correct in terms of usable Pokemon.